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Second sound and the superfluid fraction in a Fermi gas with resonant interactions


Superfluidity is a macroscopic quantum phenomenon occurring in systems as diverse as liquid helium and neutron stars. It occurs below a critical temperature1,2 and leads to peculiar behaviour such as frictionless flow, the formation of quantized vortices and quenching of the moment of inertia. Ultracold atomic gases offer control of interactions and external confinement, providing unique opportunities to explore superfluid phenomena. Many such (finite-temperature) phenomena can be explained in terms of a two-fluid mixture3,4 comprising a normal component, which behaves like an ordinary fluid, and a superfluid component with zero viscosity and zero entropy. The two-component nature of a superfluid is manifest in ‘second sound’, an entropy wave in which the superfluid and the non-superfluid components oscillate with opposite phases (as opposed to ordinary ‘first sound’, where they oscillate in phase). Here we report the observation of second sound in an ultracold Fermi gas with resonant interactions. The speed of second sound depends explicitly on the value of the superfluid fraction5, a quantity that is sensitive to the spectrum of elementary excitations6. Our measurements allow us to extract the temperature dependence of the superfluid fraction, a previously inaccessible quantity that will provide a benchmark for theories of strongly interacting quantum gases.

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Figure 1: Observing the propagation of first and second sound.
Figure 2: Extracting the sound speeds.
Figure 3: Normalized sound speeds and the 1D superfluid fraction.
Figure 4: Superfluid fraction for the homogeneous case.


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We thank E. R. Sánchez Guajardo for his contributions in the early stage of this work, and P. van der Straten for discussions. The Innsbruck team acknowledges support from the Austrian Science Fund (FWF) within SFB FoQuS (project no. F4004-N16). The Trento team acknowledges support from the European Research Council through the project QGBE and from the Provincia Autonoma di Trento. We dedicate the present work to our late friend and colleague A. Griffin, who enthusiastically promoted the idea of measuring second sound in Fermi gases.

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L.A.S. and M.K.T. equally contributed to the experimental work and the data analysis under the supervision of R.G. The new experimental methods were conceived by these three authors jointly. The theoretical work was performed by Y.-H.H., L.P. and S.S.

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Correspondence to Meng Khoon Tey.

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The authors declare no competing financial interests.

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Sidorenkov, L., Tey, M., Grimm, R. et al. Second sound and the superfluid fraction in a Fermi gas with resonant interactions. Nature 498, 78–81 (2013).

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